Whether you're playing football or just watching, much of the fun lies in the game's unpredictability. Who isn't excited by a slippery runner who dodges half of the other team, a desperate pass that turns a potential sack into a long gain or a critical fumble that transforms despair into hope -- or vice versa?
If the game is unpredictable, the physical processes behind it are not. They're as certain as the sunrise. Although science may not help you guess your opponent's next move, it sure can help you to understand the possibilities.
Suppose that you've just thrown the football and it's spiraling away from you. You're no longer touching it. So what keeps the ball moving forward? It's inertia, the universal tendency of things that are moving to keep moving, and of things at rest to remain at rest.
The football is simply coasting. In fact, were it not for gravity and air resistance, the football would coast forward forever in a straight line, and someone on the space shuttle would have to complete the pass play. Fortunately, gravity bends the ball's path
into a downward arc that brings it to the hands of the receiver but not before the ball has spent some time in flight and traveled a considerable distance downfield. Touchdown!
What determines how long the ball stays up and how far it goes? Here, we must be a bit technical.
First, flight time depends on how fast the football is gaining altitude when it leaves your hand. At that instant, the downward force of gravity begins sapping the upward motion of the ball, eventually stopping it completely -- right at the top of the smooth curve of a pass or kick.
The faster the ball is rising initially, the longer it coasts upward before gravity stops its rise and returns it to Earth. Doubling the ball's initial upward speed doubles its time aloft [see illustration].
Second, the pass's downfield distance depends on this flight time and on how fast the ball moves. Since gravity doesn't affect the ball's horizontal speed, the ball coasts steadily downfield during flight. Doubling either flight time or downfield speed will make it travel twice as far downfield before it lands.
In the moments before you release the football, you go through this sort of analysis without even being aware of it. You decide the ball's flight time and distance, and you throw accordingly. If you choose a short bullet pass, you aim the ball almost horizontally so it travels quickly during its brief flight.
If you choose a long bomb, you aim about 45 degrees above horizontal so the football arcs high and long, traveling downfield at a moderate pace during its leisurely flight.
If you have to punt, you want two somewhat incompatible things to happen at the same time. On the one hand, you want the ball to go fairly far downfield. But you also want it to stay in the air for a long enough "hang time" so your teammates can be closer to your opponents when one of them catches the ball.
You'll get maximum distance with a 45-degree kick but not the longest hang time. You'll get maximum hang time by kicking the ball straight up but no distance at all. Then the ball would either hit you on the head or give your opponents excellent field position. (It's best to save jump balls for basketball.) You'll no doubt choose something in between.
What a Drag
So far, we've ignored air's effects on the flight of a football. In fact, a properly thrown spiral pass flies like an oddly shaped glider. With its nose higher than its tail, the ball pushes downward on air rushing past it, and that air responds by pushing upward on the ball: action and reaction.
This upward push partly balances the ball's weight so it falls less quickly and stays aloft longer. That's one reason that a good spiral travels farther than a wobbling throw.
The other reason is that a wobbling football encounters more air resistance. As it arcs through the air, the ball leaves behind a swirling wake of invisible turbulence. Creating that wake costs energy and slows the ball, so it's important to keep the wake as small as possible. Since a wobbling pass produces a larger wake than a perfect spiral, the ball slows more quickly and doesn't travel as far.
Wouldn't it be nice if a wobbling football would quickly evolve into a spiral? Sadly enough, physics prevents this. In addition to its ordinary inertia, a football has rotational inertia: If it's rotating in a particular way, it tends to continue rotating that way, which is why you never see a spinning yo-yo suddenly change its angle or direction of spin.
Part of the skill in throwing a football involves setting it spinning just right as it leaves your fingers. Once the football is on its own, its spin is fixed, for better or worse. In the best case, rotational inertia keeps the ball moving with its nose up, gaining a little distance from "lift."
Actually, air twists the flying football slightly and thus has a small influence on its rotation that could tend to reduce drag. However, an end-over-end throw isn't going improve much in flight. That's because the rotating football acts as a gyroscope and resists the air's efforts to change its spin. But a spinless throw lacks such gyroscopic stability, and the ball flutters awkwardly.
Even if you throw the ball perfectly, your range is limited. What makes it so difficult to outthrow an NFL quarterback? The answer is power.
When you throw, arm and shoulder muscles are transferring energy to the ball at a tremendous rate defined by the power those muscles generate. But increasing your throwing distance requires more than a proportional increase in muscle power, particularly when air resistance is taken into account.
In fact, when Redskins quarterback Brad Johnson throws the football twice as far as you do, he is producing roughly four times as much power. No wonder they pay him the big bucks.
Passing doesn't always work, so sometimes you have to run with the football. Now you're in direct control of the ball, but you still can't avoid physics. If you make the mistake of stopping and letting a lineman who outweighs you by 100 pounds plow into you at full speed, you're going to find yourself moving backward rather abruptly.
Actually, it's not really a matter of weight but of mass, the quantity of stuff he contains. Sure, that opponent weighs a lot, and you don't want him to step on your toes. But he also has a lot of mass, meaning that he's difficult to accelerate.
Acceleration occurs when the velocity of something is altered -- that is, when it slows down, speeds up or changes direction. If you walked to the opposing team's huddle and tried to shake that massive bruiser back and forth, you'd find him very resistant to your efforts. As you pushed him from side to side, he'd push back -- action and reaction again -- and you'd find yourself shaking more than him.
It would be physics, not fear, that makes you shake, at least until he begins to chase you across the field.
FORCE AND MASS
Massive objects have more inertia and are more difficult to accelerate than less massive objects. So when you collide with the big guy during your run, you'll both push on one another, but you're going to do more accelerating.
Fortunately, his mass makes him more than just unpleasant to hit. It also makes him less agile. The more mass something has, the more force it takes to accelerate it. So if he wants to change his velocity in order to follow as you turn suddenly to the left, he'll need a larger leftward force than a smaller player would.
He obtains that force by pushing rightward on the ground so that the ground pushes leftward on him. Thus, he accelerates leftward to meet you but not as fast as he would if he weren't carrying that extra mass.
You just have to hope that the extra mass is fat, not muscle. If it's muscle, he can probably summon such enormous forces from the ground that he'll catch you anyway. Then you're back to the bone-jarring collision.
It's now easy to see why football players strengthen their legs -- not just to support their weight or that of would-be tacklers. It's also to allow rapid acceleration in any direction.
If your legs can support three times your weight, you can accelerate sideways at up to 3 gs, three times the acceleration due to gravity. If you can change your velocity that fast, you'll be able to dance away from many potential tackles.
But to accelerate like that, you'll need spiked shoes because friction alone won't let you push sideways hard enough. On ordinary grass or artificial turf, conventional athletic shoes skid easily. Spikes dig into the ground so your feet remain planted as you leap sideways to avoid a collision.
Suddenly a hole opens, and you're in the clear. Only one player stands between you and the end zone. He won't let you pass without a fight, so you're destined to have some sort of encounter. Should you run into him as fast as possible? Or slow down and try to push through him?
The answer depends a bit on what your opponent has in store for you and how much control you'll need over your motion. When you're moving, you carry an important quantity known as momentum, which depends on your mass and your velocity. Unless you can somehow gain weight while running downfield, however, the only way to increase your momentum is to go faster.
Momentum has a direction, and right now, your momentum points toward the goal line. For your opponent to stop you completely, he must extract all of your forward momentum. He can't just make your momentum disappear because momentum is a "conserved" quantity. It can't be created or destroyed. So if you've got forward momentum, the only way to lose it is to transfer it to something else.
Your opponent has three choices. He can try to absorb your momentum himself. He can try to make you transfer it to the ground. Or he can add to your momentum in such a way that it carries you out of bounds.
Let's examine each option. First, suppose he tries to absorb your momentum himself by letting you hit him directly. During the collision, you push him forward and increase his forward momentum while he pushes you backward and decreases your forward momentum.
Overall, you transfer a certain amount of your forward momentum to him. Assuming that the two of you don't bounce much when you collide, the result is simple -- the more forward momentum you have before you hit, the more forward momentum you'll have when it's over. In a head-on collision, you want to maximize your forward momentum by maximizing your forward speed [see illustration at left].
Second, suppose he tries to make you transfer your momentum to the ground by knocking your feet out from under you. As you skid along the grass, it pushes backward on you, and your forward momentum gradually decreases.
Ideally, you'd like to avoid being tripped, and that may involve decreasing your speed a bit to give you more control. But if you know you're going down, you might as well be traveling fast. That way you'll be farther downfield when the play ends.
Finally, what happens if he tries to steer you out of bounds? Now he's using your momentum against you. When you're running straight downfield near the sideline, you have considerable downfield momentum and are difficult to stop. But you're not difficult to steer.
A shove directly toward the sideline will redirect your momentum slightly. Instead of heading straight toward the end zone, you'll be heading off the field at an angle that depends on how hard you were shoved.
You can push on the ground to compensate. But if you're going fast, you won't have much time to regain your course. In a second or two, you'll find yourself transferring momentum with the waterboy.
To avoid this sort of trouble, you can slow down so that you have longer to recover from a side blow. But it's a gamble because, with a fast forward speed, at least you'll be well downfield when you do go out of bounds. If you slow and are tackled or knocked out of bounds, your teammates won't let you forget it.
Gearing Up
Spiked shoes aren't the only equipment you need. It helps to wear padding and a helmet. Sure, they make you look cool, but they also make you more comfortable and may save your life.
Suppose that two players are running toward one another at full speed and collide headfirst. Suppose, too, that neither is wearing a helmet. What happens?
Their foreheads touch and begin to push apart vigorously. After all, two foreheads can't occupy the same space at the same time. There isn't much time to stop the heads from moving into one another, so the forces that decelerate them are tremendous. As the two heads come suddenly to a stop, skin bruises and bones bend. This won't look good in the morning.
But more importantly, the soft gray tissue inside their heads doesn't stop so quickly. A brain is somewhat independent of the skull around it and, under certain circumstances, can slosh about. In a forehead collision, the brain coasts forward because of its inertia, and it doesn't stop until it collides with the now stationary skull in front of it. This internal impact leads to a concussion or worse.
You want to slow that acceleration so the forces are smaller and nothing is damaged. If those two players were wearing helmets, the story would be different. Each head would still stop after they collided, but everything would be slower and gentler.
Padding in a helmet prolongs deceleration so the forces involved aren't as large at any given moment. It also spreads those weaker forces over lots of skin so there isn't even a bruise. Furthermore, there's probably no concussion because skull and brain slow more or less together.
The same reasoning applies to body pads. They spread the forces of impact over time and space so that they don't cause local injury. Think of them as airbags for body parts. Pads won't prevent you from stopping if you run into the goal post after a dramatic catch, but you'll stop more slowly, and it won't hurt as much. You'll be able to enjoy the victory celebration.
Louis A. Bloomfield teaches physics at the University of Virginia. He is the author of How Things Work: The Physics of Everyday Life (1996).
To gain maximum distance on a throw or kick, the ball should be launched at about a 45-degree angle. But the distance is much greater if the ball travels nose-first (for minimum air drag) rather than end-over-end (producing four times more drag).
Launching Distance in yards
Angle End-over-end Nose-first
45 37 55
50 36 54
55 34 51
60 31 47
Punts and kickoffs involve a trade-off between distance, which is greatest at about a 45-degree angle, and hang time, which increases with steeper angles but at the expense of distance.
AT 60 mph
Launching Distance Hang time
Angle (yards) (seconds)
43 64 3.49
50 62 3.90
55 59 4.16
60 54 4.39
SOURCES: Sports Science by Peter J. Brancazio
What happens when push comes to shove? That depends on your mass and your speed -- that is, your momentum -- and the momentum of the person you hit. The total amount of momentum is always the same before and after a collision. Knowing that, you can predict the outcome. For example, if a 176-pound defender running west at 17 mph tackles a 224-pound fullback running east at 15 mph, which way will their entwined bodies travel after a head-on collision? The fullback has 12 percent more momentum than the defender. So they'll move east at 1.27 feet per second.
SOURCE: Sports Science by Peter J. Brancazio
